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Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods

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  • Karaaslan, Mehmet Fatih
  • Celiker, Fatih
  • Kurulay, Muhammet

Abstract

In this paper, we introduce a hybridizable discontinuous Galerkin method for numerically solving a boundary value problem associated with the Bagley–Torvik equation that arises in the study of the motion of a plate immersed in a Newtonian fluid. One of the main features of these methods is that they are efficiently implementable since it is possible to eliminate all internal degrees of freedom and obtain a global linear system that only involves unknowns at the element interfaces. We display the results of a series of numerical experiments to ascertain the performance of the method.

Suggested Citation

  • Karaaslan, Mehmet Fatih & Celiker, Fatih & Kurulay, Muhammet, 2016. "Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 51-58.
    • Handle: RePEc:eee:apmaco:v:285:y:2016:i:c:p:51-58
    DOI: 10.1016/j.amc.2016.03.024
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    Cited by:

    1. Moghaddam, B.P. & Machado, J.A.T. & Behforooz, H., 2017. "An integro quadratic spline approach for a class of variable-order fractional initial value problems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 354-360.
    2. Fathy, Mohamed & Abdelgaber, K.M., 2022. "Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Muhammed I. Syam & Azza Alsuwaidi & Asia Alneyadi & Safa Al Refai & Sondos Al Khaldi, 2018. "An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem," Mathematics, MDPI, vol. 6(7), pages 1-11, June.
    4. Zhao, Jingjun & Zhao, Wenjiao & Xu, Yang, 2023. "Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 442(C).

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